Basic properties
| Modulus: | \(4598\) | |
| Conductor: | \(2299\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(495\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2299}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4598.bs
\(\chi_{4598}(5,\cdot)\) \(\chi_{4598}(25,\cdot)\) \(\chi_{4598}(47,\cdot)\) \(\chi_{4598}(93,\cdot)\) \(\chi_{4598}(119,\cdot)\) \(\chi_{4598}(137,\cdot)\) \(\chi_{4598}(157,\cdot)\) \(\chi_{4598}(169,\cdot)\) \(\chi_{4598}(207,\cdot)\) \(\chi_{4598}(213,\cdot)\) \(\chi_{4598}(225,\cdot)\) \(\chi_{4598}(289,\cdot)\) \(\chi_{4598}(291,\cdot)\) \(\chi_{4598}(301,\cdot)\) \(\chi_{4598}(313,\cdot)\) \(\chi_{4598}(339,\cdot)\) \(\chi_{4598}(367,\cdot)\) \(\chi_{4598}(377,\cdot)\) \(\chi_{4598}(389,\cdot)\) \(\chi_{4598}(405,\cdot)\) \(\chi_{4598}(423,\cdot)\) \(\chi_{4598}(427,\cdot)\) \(\chi_{4598}(443,\cdot)\) \(\chi_{4598}(465,\cdot)\) \(\chi_{4598}(499,\cdot)\) \(\chi_{4598}(537,\cdot)\) \(\chi_{4598}(555,\cdot)\) \(\chi_{4598}(575,\cdot)\) \(\chi_{4598}(587,\cdot)\) \(\chi_{4598}(625,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{495})$ |
| Fixed field: | Number field defined by a degree 495 polynomial (not computed) |
Values on generators
\((3269,3631)\) → \((e\left(\frac{37}{55}\right),e\left(\frac{8}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 4598 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{45}\right)\) | \(e\left(\frac{2}{495}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{23}{45}\right)\) | \(e\left(\frac{193}{495}\right)\) | \(e\left(\frac{376}{495}\right)\) | \(e\left(\frac{422}{495}\right)\) | \(e\left(\frac{79}{99}\right)\) | \(e\left(\frac{86}{99}\right)\) | \(e\left(\frac{4}{495}\right)\) |